Summary of the results

1. Observations following the method of EÖTVÖS If we take f in Newton’s formula

to be dependent on the material of the attracted body and if we set

then we can represent the results of our observations through the specific attraction coefficient κ, which is deduced from these observations. Following now are the values of κ–κ_Pt with the mean errors in their calculation, where κ_Pt = 0, if f_Pt = f₀.

The mean values found for κ–κ_Pt are smaller in four cases, larger in three cases, as their mean error, and in one case they are the same.

The probability, that the quantity is non-zero, is even in these cases nearly vanishing, because a review of the corresponding data of larger series shows nearly constant deviations from the mean value whose influence on this mean can be reduced only through even longer continued observations.

The bodies under observation have very different specific weight, different molecular weights and molecular volume. Also they have different states of matter and different structure.

We believe that we are allowed to state, that regarding the attraction of the Earth, does not reach for all of these bodies the value of 0.005•10^-6.

Regarding the question, whether the attraction changed because of a chemical reaction or dissolution in the attracted body, we get an even smaller limiting value.

The reason for this is, that we found for LANDOLT’s silversulphate—iron-sulphate reaction

and for the dissolution of copper sulphate in water using the HEYDWEILLER ratio

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2. Observations in the meridian For the attraction of the Sun we found

3. Observations, regarding an influence similar to absorption or the attraction through intermediate bodies

From the experiments with the gravitation compensator (a special sensitiv torsion balance) we deduce, that a lead layer of 5 cm thickness will not cause an absorption, which reaches the value of 0.00002•10^-6.

Correspondingly: absorption of a lead layer of 1 m thickness < 0.0004•10^-6 Earth attraction, absorption through the Earth along its diameter < 1/800 Earth attraction.

4. Observations with radioactive substances

From the experiments with a radium preparation of 0.20 g weight we get¹⁶

From the experiments with another preparation we saw,

a) that it does not have any specific attraction and repulsion on a platinum cylinder of 30 g weight at a distance of 4 mm, which would reach an order of 10^-6;

b) that the preparation has no noticeable absorption on the Earth’s attraction.

With a few words we can summarize the final results of our work. We have made a series of observations, which are more exact than any of the previous ones. But in no case could we see a noticeable change from the law of proportionality of inertia and gravity.

(Manuscript received February 27, 1922) 16 The Translators suggest a positive sign.

Inertia and Gravity of Matter

by Pál SELÉNYI

(Hungarica Acta Physica, 1, 1949. 7-11)

Summary: It follows from Eötvös’ simple considerations underlying his famous experiment on the proportionality of inertia and gravity of matter that a body floating freely on a surface of water at rest could not be in equilibrium, were its constant of gravity different of that of the water, because the direction of its weight in this case would not be perpendicular to the surface of the water. As a consequence the body had to move northward or southward (to the poles or to the equator) accordingly whether its constant of gravity is supposed to be greater or lesser than that of the water, and on the same ground the rotation of a celestial body would cause the separation of the various substances constituting it. – In a preliminary report on this subject [2]

observations on the first phenomenon had been described presenting at the same time a new experimental method for proving Newton’s law of the proportionality of gravity and inertia, which even in our crude experiment went beyond the accuracy of 1 : 60 000 of Bessel’s classical pendulum experiments. – In the present paper dealing with the same subject from a more general point of view, the author would like to emphasize the importance of the above conclusions laying particular stress on the non-existence of the mechanical effect in question, which he regards to be the most simple and most direct proof of the validity of Newton’s law elucidating at the same time the important role of this law in the constitution of the Universe.

... We wish finally to point out the passages in Eötvös’ papers related with our subject. In paper [l] dealing with the theory of his well known experiment quoted above, he calculates on pages 15-16 for different values of a supposed specific gravity the extremely small angle between the directions of the two ’verticals’ belonging to two different substances and he remarks that „in that case the plumb-line would in general, not be perpendicular to the surface of licluid at rest“, but he doesn’t mention the consequence of this as to the behaviour of a floating body. We would like to emphasize for the rest, that our considerations and the above experiment had been suggested at an earlier date by Eötvös’ paper: „Geodetic Researches in Hungary, particulary those carried out with the aid of the torsional balance“. (Report presented to the XVIth General Meeting of the International Association of Geodesy, London and Cambridge, 1909) At the end of this paper, after stating that if there exists any difference at all in

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the constants of gravity of the substances examined, such difference must, in accordance with his experiments, be smaller than one part in hundred million, he says:

„It follows that two equipotential surfaces, belonging to two different substances and touching each other at the equator, will not diverge more than 0.014 cm on the poles“, and he adds: „Even if the physicist, by successive improvement of his methods of research, should in the future discover more minute traces of a selective gravity, the geodesist would confine himself to the determination of a single geoid, common for all substances.“ As appears from this quotation, this line of thought was only one step short of our experiment, this step being to ask, what will happen to a body if it is placed on an equipotential surface which is not its own.

September 6, 1948. University of Göttingen. On page 14 Eötvös deals with the influence of a specific gravity on the form of the equipotential surfaces of the weight. Let g resp. g’ = g(1–k) be the values of the acceleration of free fall for two different substances. Their equipotential surfaces, touching each other at the equator, will diverge in this case on the poles by

Let e.g. x=1/20 000 000 then z = –0.069 cm.

Eötvös remarks moreover that positive values of x correspond to an elevation, negative ones to a depression on the poles, and he goes on saying: „One might imagine such a secretion of terrestrial substances, namely an accumulation of substances with positive x on the poles, and of those with negative x in the enviroment of the equator, but the eventual effective forces are certainly too small and the resistances against these too great to render such a separation possible.”

This sentence, never published, contains apparently the last step of the conclusions we missed in Eötvös’ papers, but even here the subject was treated by him rather practically and experimentally and not from the point of view of principles.

7. Házi feladat

Feltehetően Eötvöstől származik az a fizikaszakmódszertani elv, hogy a „képlet-igazoló” demonstrációs kísérleteknél egyszerre mindig csak egy fizikai mennyiséget szabad változtatni. Eötvös, az ingák mestere szerkesztett egy igen egyszerű és ötletes eszközt a fizikai inga lengésidőképletének (T) igazolására.

,

ahol Θ az inga tehetetlenségi nyomatéka, mg a súlya és s a forgási tengely és az inga súlypontjának távolsága. Eötvös elérte, hogy Θ (és természetesen mg) változása nélkül tudta az s-t változtatni.

Hogyan csinálhatta?

(A feladat megoldása megtalálható a Báró Eötvös Loránd Emlékkönyvben Rybár István írásában a 247. oldalon.)

Problem

Construct equipment to investigate the swing-time of a physical pendulum. The formula:

,

where Θ is the inertial momentum, mg is the weight of the pendulum and s is the distance between the rotation axis and the center of the pendulum’s mass.

Vary the value of s, while leaving the value of Θ and of corse the mg constant (in the demonstration experiment it is very important that only one value at a time be varied).

Could you solve this problem? Eötvös did.

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Eötvös-csúcs a Dolomitokban Eötvös-peak in Italy

A megtalált Eötvös-szobor Szarvason We found this statue at Szarvas